Determination of the first and second normal stress differences in the truncated-cone-and-plate apparatus

Summary

The steady state radial pressure distribution in the truncated cone-and-plate (TCP) apparatus has been measured for a highly elastic polyisobutylene solution in cis-trans decalin (M_W=4300 kgmol⁻¹ M_W/M_n=2) at eight shear rates from 1 to 270 s⁻¹ and temperatures of 3.0, 20.0, 30.0 and 46.0° C. The slope of pressure, corrected for inertia by the classical formula, versus the logarithm of radius provides a combination of normal stress differences N₁+2N₂ with a typical experimental scatter of 1 % at all measured temperatures and shear rates. The plots of N₁+2N₂ versus shear rate can be shifted, without loss of accuracy, by means of the time-temperature superposition principle, the shift factors strictly adhering to a WLF equation. Extrapolated rim pressures, when corrected for elastic hole pressure with a theoretical equation, give values of the second normal stress difference with typically less than 10 % of experimental scatter. Contrary to previous analyses of the TCP apparatus, the center-hole pressure is found to give a useful estimate of the second normal stress difference, although there are insufficient data at present to perform the differentiation of a nonlinear function required in the analysis of the data. Instrument imperfections are reviewed briefly in the Appendix.